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Numbers k such that A011772(k) does not divide A344875(k).
3

%I #11 Jun 05 2021 16:44:30

%S 12,14,15,20,22,30,33,35,38,42,44,45,46,48,51,52,54,56,60,62,63,65,66,

%T 69,70,72,76,77,80,84,85,86,87,88,90,91,92,94,95,99,102,104,105,108,

%U 110,112,114,115,116,117,118,119,123,124,126,130,132,133,134,135,138,140,141,142,143,144,145,148,152,153,154,156

%N Numbers k such that A011772(k) does not divide A344875(k).

%C The first term not in A344883 is 60. First terms included in A344883, but not here are: 900, 1260, 1560, 3740, 6552, 6669, etc. (A344694). See also comments in A344975.

%o (PARI)

%o A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772

%o A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };

%o isA344980(n) = (A344875(n)%A011772(n));

%Y Cf. A011772, A344694, A344875, A344975.

%Y Complement of A344974. Positions of nonzero terms in A344973, and of terms > 1 in A344970.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 05 2021